Preference-based evolutionary multi-objective optimization for solving fuzzy portfolio selection problems

• Ana Belén Ruiz Mora ^[1] ; Rubén Saborido ^[2] ; José D. Bermúdez ^[3] ; Mariano Luque ; ENRIQUETA VERCHER ^[3]
  1. [1] Universidad de Málaga

     Universidad de Málaga

     Málaga, España

     
  2. [2] Ecole Polytechnique de Montréal

     Ecole Polytechnique de Montréal

     Canadá

     
  3. [3] Universitat de València

     Universitat de València

     Valencia, España

     

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• Localización: Rect@: Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA, ISSN-e 1575-605X, Vol. 18, Nº. 1, 2017, págs. 1-15
• Idioma: inglés
• DOI: 10.24309/recta.2017.18.1.01
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    En este trabajo, abordamos el problema de selección de carteras de inversión desde una perspectiva multiobjetivo y consideramos algoritmos evolutivos de optimización multiobjetivo basados en preferencias para generar carteras eficientes teniendo en cuenta preferencias del inversor. Por un lado, proponemos un modelo de optimización para la selección de carteras con tres objetivos, en el que se han considerado números fuzzy de tipo LR para modelizar la incertidumbre de los futuros beneficios. Las funciones objetivo a optimizar son el beneficio esperado (a maximizar) y dos medidas del riesgo de la inversión (ambas a minimizar): la semi-desviación media absoluta por debajo del beneficio esperado y el valor de riesgo (medida de la peor pérdida esperada en un horizonte dado). Además de la restricción presupuestaria, se ha introducido una restricción que limita la cardinalidad de las carteras y cotas superiores e inferiores para la inversión en cada activo. El problema de optimizatión multiobjetivo resultante, denominado por sus siglas en inglés como modelo MASdVaR (mean-absolute semi-deviation value-at-risk model), es no lineal y no convexo y, por ello, se ha aplicado el algoritmo evolutivo basado en preferencias WASF-GA para generar carteras de inversión eficientes. En WASF-GA, se consideran valores de aspiración que el decisor desea alcanzar en cada objetivo para expresar las preferencias. Para el modelo MASdVaR, los valores de aspiración considerados corresponden a un perfil de inversor conservador. Los resultados obtenidos para un caso basado en el mercado de inversión español demuestran que las carteras eficientes obtenidas que alcanzan los mayores beneficios, mejoran los valores de referencia considerados para las dos medidas del riesgo. Por otro lado, aquellas carteras con beneficios más moderados presentan valores de riesgo menores, pero sin dejar de satisfacer las aspiraciones del inversor, por lo que representan estrategias de inversión menos arriesgadas.

  • English

    In this work, we address the multi-criteria paradigm of the portfolio selection problem and consider a preference-based evolutionary multi-objective optimization algorithm to find Pareto optimal portfolio solutions based on the investor preferences. Firstly, we propose a three-objective optimization model for portfolio selection, in which the uncertainty of the portfolio returns is modelled by means of an LR-power fuzzy variable. In the model, three criteria are considered, which are the credibility expected value of the returns (to be maximized) and two measures of the risk (both to be minimized): the belowmean absolute semi-deviation and the fuzzy value-at-risk. Besides the budget constraint, a cardinality constraint and lower and upper bound constraints for the assets are also considered. The resulting model, called a credibility mean-absolute semi-deviation value-at-risk (MASdVaR) model, is a non-linear and nonconvex multi-objective optimization problem which is solved by means of the preference-based evolutionary algorithm WASF-GA. In WASF-GA, the preferences are expressed by means of aspiration values that the decision maker would like to achieve for the objectives. In the MASdVaR model, the investor aspiration values considered for the objectives are calculated assuming a conservative profile. The results obtained for a case study based on the Spanish stock market show that the portfolios generated with the highest expected returns improve the aspiration values considered for the two risk measures. Besides, portfolios with intermediate values for the expected return achieve lower values for the risk measures, but they still improve their aspiration values and thus represent less risky investment options for the investor.

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